Section 10A notes.notebook
April 04, 2016
Section 10A: Arithmetic Sequences Goal: Develop understanding of the nomenclature of sequences and understanding of arithmetic sequences in particular.
Determine the next 3 values in the pattern: 1] 2, 4, 6, ____, ____, ____ 2] 10, 5, 0, -5, ____, ____, ____ 3]
____, ____, ____
The numbers are ordered so that it has a first member, a second member, a third member and so on.
numbers in a sequence
terms
function whose domain is a set of sequence consecutive integers if domain is not stated, it is understood that the domain starts with 1
the terms in the sequence
term 3
finite sequence
term 2
term 1
sequence with a last term
gives the relative position of each domain term:1st, 2nd, 3rd, and so on
Sequence 1: 5, 10, 15, 20, 25
sequence that continues without stopping
infinite sequence
Sequence 2: 5, 10, 15, 20, 25, ... a1 a2 a3
?
Which sequence is finite? Infinite? What rule would represent the sequences?
range
Section 10A notes.notebook Use the given rule to write the first 6 terms of the sequence: 4] an = 2n + 3 5]
April 04, 2016 sequence in which the difference arithmetic between consecutive terms is sequence constant constant difference d
To decide if a sequence is arithmetic, you need to
Decide whether each sequence is arithmetic. 6] -3, 1, 5, 9, 13, ...
How can we write rules for arithmetic sequences? 5, 8, 11, 14, 17, ...
8, 3, -2, -7, -12, -17, ...
common difference
7] 2, 5, 10, 17, 26, ...
Rule for an Arithmetic Sequence
The nth term of an arithmetic sequence with first term a1 and common difference d or is given by:
Section 10A notes.notebook
Write a rule for the arithmetic sequence and then find a25. 8] 50, 44, 38, 32, ...
April 04, 2016
10] One term of an arithmetic sequence is a13=30. The common difference is d = Write a rule for the nth term. This is known as an explicit rule.
9]
11] a12 = -4 d = -6
12] Write a rule for the nth term if a6 = 10 and a21 = 55.
13] a10 = 8 and a16 = 32
14] a0=22 and a10 = 37
Homework: Worksheet 10A Unit 10 Quiz on Wednesday, April 13, for period 4 and Thursday, April 14, for period 5. Questions on worksheets 9N and 9O answered on Wednesday, April 6, with the Unit 9 Quiz #3 on Friday, April 8.
